改进的和声搜索算法求绝对值方程

摘要

绝对值方程Ax-｜x｜ =b是一个不可微的NP-hard问题.给出一个改进的和声搜索算法,在种群更新过程中,采取“前拉后推”技巧来加速收敛；同时为了保持种群的多样性,在种群更新过程中以一定的概率在可行域内选取.实验结果表明,改进后的算法能够快速地求出绝对值方程尽可能多的解.%Absolute value equations Ax-｜ x｜ =b is a non-differentiable NP-hard problem.An improved harmony search is presented for solving the NP-hard absolute value equation (AVE).In the process of updating the population particles,"front pulled and back pushed" technique is taken to accelerate convergence and improve calculation accuracy.Meanwhile,in order to maintain diversity of population,the population particles in feasible region with a specified probability are updated.Numerical results show that the improved harmony search method can quickly get as many solutions to the absolute value equation as possible.